Abstract:
Hypocoercivity based analysis is a powerful tool for kinetic equations which allows one to understand the regularity and long-time behavior of both linear and nonlinear kinetic equations, despite that kinetic operators are degeneratedly disipative. We extend such analysis to linear and nonlinear kinetic equations with random uncertainties in initial data or collisional kernels, which allows us to establish regularity, local sensitivity with respect to uncertain random parameters, and long-time exponential decay of the solution toward the global equilibrium in the random space, as well as spectral convergence and long-time error decay of the polynomial chaos based stochastic Galerkin methods, a popular method used for uncertainty quantification.
Biography:
Shi Jin, Director of Institute of Natural Sciences, Shanghai Jiao Tong University. He received his B.S. from Peking University, and his Ph.D. from University of Arizona. He has been a Postdoc at Courant Institute, New York University, an Assistant and Associate Professor at Georgia Institute of Technology, Professor, Department Chair, and Vilas Distinguished Achievement Professor at University of Wisconsin-Madison, Chair Professor, Chair of Department of Mathematics, and Director of Institute of Natural Sciences, Shanghai Jiao Tong University.
Among the honors he received include the Feng Kang Prize in Scientific Computing, Excellent Young Researcher Award by Natural Science Foundation of China (Class B), Changjiang Visiting Professorship (at Tsinghua University), Morningside Silver Medal at International Congress of Chinese Mathematicians, inaugural Fellow of the American Mathematical Society (AMS), Fellow of Society of Industrial and Applied Mathematics (SIAM), and invited lecture at International Congress of Mathematicians in 2018.
Shi Jin’s research interests include kinetic theory, hyperbolic conservation laws, high frequency wave computation, quantum dynamics, uncertainty quantification, and multiscale computation of physical problems. He has published more than 160 research papers in these areas.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai